Given $ m \angle MON = 7x - 63$, $ m \angle LOM = 4x - 21$, and $ m \angle LON = 48$, find $m\angle LOM$. $O$ $L$ $N$ $M$
Solution: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Substitute in the expressions that were given for each measure: $ {4x - 21} + {7x - 63} = {48}$ Combine like terms: $ 11x - 84 = 48$ Add $84$ to both sides: $ 11x = 132$ Divide both sides by $11$ to find $x$ $ x = 12$ Substitute $12$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 4({12}) - 21$ Simplify: $ {m\angle LOM = 48 - 21}$ So ${m\angle LOM = 27}$.